A connecting block of the above mentioned type is known in the art from German Patent DE-PS 32 01 894. The connecting block comprises three block bodies, which are placed one on top of the other, and are plugged onto tongues extending through latch devices at the two front sides of the block bodies. The upper and lower block bodies are provided with insulation displacement contact elements, which are arranged one behind the other in a line. Each insulation displacement contact comprises two resilient contact legs limiting a central contact slot. An insulated cable conductor to be wired is pressed by means of a tool into the contact slot. The sharp edges of the contact legs cutting through the insulation of the cable conductor, and establishing an electrical contact with the conductive core of the cable conductor. Inserting and pressing-in of the insulated cable conductor into the contact slot is performed from the top of the each block body in the direction of its bottom side. For connecting a cable conductor, the top side or connection side of each block body must therefore be left free. With the known connecting block, it is disadvantageous when connecting the insulated cable conductors to the insulation displacement contact element of the central block body, that first the upper block body has to be removed from the tongues. Then, only, the top side of the central block body is accessible, in order to establish the contact of the cable conductors with the insulation displacement contact elements. Later rearrangements of the cable conductors connected already to the central block body are not possible, since the cable conductors connected to the upper block body prevent the removal of the upper block body. Furthermore, the lateral tongues for plugging the three block bodies on are required as additional components.